The above table represents a consumer buying two goods, Pizza and Milk shakes. The price of a Pizza is 2.00 per unit and a Milkshake is 1.00 per unit. The consumer's income is $8.00 and is all spent. Answer the following questions.

• MU of 1st Pizza ($MU_{P1}$) = 36 utils
• MU of 1st Milkshake ($MU_{M1}$) = 30 utils
• MU of 2nd Milkshake ($MU_{M2}$) = 22 utils

The consumer's total satisfaction from consuming 1 pizza and two milkshakes is $\boxed{\text{88 utils}}$.

12. ii. Show the best way for this consumer to spend his income in order to maximize his satisfaction.

The consumer's income is $8.00. The price of Pizza ($P_P$) is$2.00, and the price of a Milkshake ($P_M$) is $1.00. To maximize satisfaction, the consumer must equate the marginal utility per dollar spent for both goods ($MU_P/P_P = MU_M/P_M$) and spend all income.

• 1st unit: Milkshake (30 utils/$) - Cost$1.00. Remaining income: $7.00. (Qp=0, Qm=1)
• 2nd unit: Pizza (18 utils/$) - Cost$2.00. Remaining income: $5.00. (Qp=1, Qm=1)
• 3rd unit: Milkshake (22 utils/$) - Cost$1.00. Remaining income: $4.00. (Qp=1, Qm=2)
• 4th unit: Milkshake (16 utils/$) - Cost$1.00. Remaining income: $3.00. (Qp=1, Qm=3)
• 5th unit: Pizza (12 utils/$) - Cost$2.00. Remaining income: $1.00. (Qp=2, Qm=3)
• 6th unit: Milkshake (12 utils/$) - Cost$1.00. Remaining income: $0.00. (Qp=2, Qm=4)

At this point, the consumer has purchased 2 Pizzas and 4 Milkshakes.
Total cost = (2 \times \2.00) + (4 \times $1.00) = $4.00 + $4.00 = $8.00$. All income is spent. The$MU/P$for the last unit of Pizza (2nd) is 12. The$MU/P$for the last unit of Milkshake (4th) is 12. The condition$MU_P/P_P = MU_M/P_M = 12$ is met.

The best way for this consumer to spend his income is to purchase $\boxed{\text{2 Pizzas and 4 Milkshakes}}$.

12. iii. What will be his total satisfaction in utils?

• Total Utility from 2 Pizzas = $MU_{P1} + MU_{P2} = 36 + 24 = 60$ utils
• Total Utility from 4 Milkshakes = $MU_{M1} + MU_{M2} + MU_{M3} + MU_{M4} = 30 + 22 + 16 + 12 = 80$ utils

His total satisfaction will be $\boxed{\text{140 utils}}$.

12. iv. State his equilibrium condition.

The consumer equilibrium condition for maximizing utility is:

And all income must be spent.
The equilibrium condition is that the $\boxed{\text{marginal utility per dollar spent on Pizza equals the marginal utility per dollar spent on Milkshake}}$.

12. v. The price of both goods now cos $1.00 each. How should this consumer spend his income?

New prices: $P_P = 1.00$, $P_M = 1.00$. Income = $8.00. The condition for utility maximization becomes$MU_P/1 = MU_M/1$, or simply$MU_P = MU_M$, and$Q_P + Q_M = 8$(since each unit costs$1.00, 8 units can be bought).

• 1st unit: Pizza (MU=36). (Qp=1, Qm=0)
• 2nd unit: Milkshake (MU=30). (Qp=1, Qm=1)
• 3rd unit: Pizza (MU=24). (Qp=2, Qm=1)
• 4th unit: Milkshake (MU=22). (Qp=2, Qm=2)
• 5th unit: Pizza (MU=20). (Qp=3, Qm=2)
• 6th unit: Pizza (MU=18). (Qp=4, Qm=2)
• 7th unit: Milkshake (MU=16). (Qp=4, Qm=3)
• 8th unit: Pizza (MU=16). (Qp=5, Qm=3)

At this point, the consumer has purchased 5 Pizzas and 3 Milkshakes.
Total units = $5 + 3 = 8$. Total cost = 8 \times \1.00 = $8.00$. All income is spent. The MU for the last unit of Pizza (5th) is 16. The MU for the last unit of Milkshake (3rd) is 16. The condition$MU_P = MU_M = 16$ is met.

The consumer should spend his income by purchasing $\boxed{\text{5 Pizzas and 3 Milkshakes}}$.

12. vi. Sketch the Demand curve for Pizza.

From part ii, when P_P = \2.00$, the quantity demanded ($Q_P$) is 2 units. From part v, when$P_P = $1.00$, the quantity demanded ($Q_P$) is 5 units.

To sketch the demand curve for Pizza:

1. Draw a graph with Price on the vertical (y) axis and Quantity on the horizontal (x) axis.
2. Plot the first point: (Quantity = 2, Price = $2.00).
3. Plot the second point: (Quantity = 5, Price = $1.00).
4. Draw a downward-sloping line connecting these two points. This line represents the demand curve for Pizza.

12. vii. Is Pizza elastic or inelastic at the above price points? Explain.

To determine elasticity, we calculate the price elasticity of demand (PED) using the midpoint formula.

• Initial Price ($P_1$) = $2.00, Initial Quantity ($Q_1$) = 2
• New Price ($P_2$) = $1.00, New Quantity ($Q_2$) = 5

Since $PED > 1$, Pizza is $\boxed{\text{elastic}}$. This means that a percentage change in price leads to a larger percentage change in quantity demanded.